The tumblers you are using are of better quality than the ones I use
(Harbor Freight) and have mine tumbling for weeks at a time. So, I
doubt that a more expensive tumbler would solve your problem.

But, I am tumbling rocks, I don’t know what you have in yours. After
one day (24 hours) I open the barrel and take a peek. The purpose of
this is to relieve gas pressure that builds up from either the rocks
and/or grit. I don’t know which and I don’t care. What I do know is
that I don’t need a mess all over the floor.

The problem you describe sounds like gas pressure. Why don’t you
open the barrel after 24 hours, and maybe 48 hours, and see if it
helps. A bulging barrel is a good indicator of gas build up, but I
wouldn’t wait that long. There are things that can be added to a
tumble mix to obviate this problem but I don’t remember what they
are, and I wouldn’t bother with them.

The tumblers you are using are of better quality than the ones
I use (Harbor Freight) and have mine tumbling for weeks at a time.
So, I doubt that a more expensive tumbler would solve your problem.

I use the same, cheap, Harbor Freight tumbler, except I only use it
with stainless steel shot for burnishing sterling silver. I load it
about 3/4 full with approximately 1 teaspoon of burnishing soap, and
fill with water about 1/4" above the shot. Never had a problem
(yet).